Tolerance analysis methods, which are important to achieve a balance between manufacturing costs and functional requirements, have been studied and improved over the last 30 years. This paper proposes a new method to improve the precision of assembly simulation for statistical assembly simulation; by investigating the effect of the geometric deviations and mechanical behaviors of assembly contact on the stack-up assembly deviation by combining the recent theories on the tolerance analysis of rigid bodies and local contact deformation. To improve the precision of the tolerance analysis, real parts with form defects were simulated with the help of non-nominal skin model shapes. The SMSs were first considered to be rigid, and a quadratic optimization-based method for the rigid body displacement was used to calculate the initial contact points of all the SMSs. Next, contact deformation, following Hertzian contact theory, occurred at the initial contact points, which changed the relative positions of the SMSs in the subsequent interactions. The iteration process was convergent, and the final simulation for tolerance analysis could be generated after several iterations. Case studies demonstrated the practicality of the proposed method. Their actual assembly deviations were simulated by combining the effects of geometric deviations and local surface deformations. Since the proposed tolerance analysis framework based on statistical assembly simulation, it is expected to control the functional requirements of mechanical assemblies with much rough tolerance design and help optimize the tolerance in the future.

公差分析方法对于在制造成本和功能要求之间取得平衡非常重要，在过去30年中已经对其进行了研究和改进。针对统计装配仿真，提出了一种提高装配仿真精度的新方法。通过结合刚体的公差分析和局部接触变形的最新理论，研究装配接触的几何偏差和机械性能对叠层装配偏差的影响。为了提高公差分析的精度，借助非名义蒙皮模型形状对具有形状缺陷的真实零件进行了模拟。SMS最初被认为是严格的，然后采用基于二次优化的刚体位移方法来计算所有SMS的初始接触点。接下来，遵循赫兹接触理论的接触变形发生在初始接触点，这改变了SMS在后续相互作用中的相对位置。迭代过程是收敛的，公差分析的最终仿真可以在多次迭代后生成。案例研究证明了该方法的实用性。通过组合几何偏差和局部表面变形的影响来模拟它们的实际装配偏差。由于建议的公差分析框架是基于统计装配模拟的，